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Improved Description of Blaschke–Santaló Diagrams via Numerical Shape Optimization 通过数值形状优化改进对布拉什克-桑塔洛图的描述
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-02 DOI: 10.1007/s00245-025-10250-w
Ilias Ftouhi
{"title":"Improved Description of Blaschke–Santaló Diagrams via Numerical Shape Optimization","authors":"Ilias Ftouhi","doi":"10.1007/s00245-025-10250-w","DOIUrl":"10.1007/s00245-025-10250-w","url":null,"abstract":"<div><p>We propose a method based on the combination of theoretical results on Blaschke–Santaló diagrams and numerical shape optimization techniques to obtain improved description of Blaschke–Santaló diagrams in the class of planar convex sets. To illustrate our approach, we study three relevant diagrams involving the perimeter <i>P</i>, the diameter <i>d</i>, the area <i>A</i> and the first eigenvalue of the Laplace operator with Dirichlet boundary condition <span>(lambda _1)</span>. The first diagram is a purely geometric one involving the triplet (<i>P</i>, <i>d</i>, <i>A</i>) and the two other diagrams involve geometric and spectral functionals, namely <span>((P,lambda _1,A))</span> and <span>((d,lambda _1,A))</span> where a strange phenomenon of non-continuity of the extremal shapes is observed.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10250-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved accuracy of an analytical approximation for option pricing under stochastic volatility models using deep learning techniques
IF 2.9 2区 数学
Computers & Mathematics with Applications Pub Date : 2025-04-02 DOI: 10.1016/j.camwa.2025.03.029
Donghyun Kim , Jeonggyu Huh , Ji-Hun Yoon
{"title":"Improved accuracy of an analytical approximation for option pricing under stochastic volatility models using deep learning techniques","authors":"Donghyun Kim ,&nbsp;Jeonggyu Huh ,&nbsp;Ji-Hun Yoon","doi":"10.1016/j.camwa.2025.03.029","DOIUrl":"10.1016/j.camwa.2025.03.029","url":null,"abstract":"<div><div>This paper addresses the challenge of pricing options under stochastic volatility (SV) models, where explicit formulae are often unavailable and parameter estimation requires extensive numerical simulations. Traditional approaches typically either rely on large volumes of historical (option) data (data-driven methods) or generate synthetic prices across wide parameter grids (model-driven methods). In both cases, the scale of data demands can be prohibitively high. We propose an alternative strategy that trains a neural network on the <em>residuals</em> between a fast but approximate pricing formula and numerically generated option prices, rather than learning the full pricing function directly. Focusing on these smaller, smoother residuals notably reduces the complexity of the learning task and lowers data requirements. We further demonstrate theoretically that the Rademacher complexity of the residual function class is significantly smaller, thereby improving generalization with fewer samples. Numerical experiments on fast mean-reverting SV models show that our residual-learning framework achieves accuracy comparable to baseline networks but uses only about one-tenth the training data. These findings highlight the potential of residual-based neural approaches to deliver efficient, accurate pricing and facilitate practical calibration of advanced SV models.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 150-165"},"PeriodicalIF":2.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-023-1062-7
Yu-ting Kang, Peng Luo, Chang-lin Xiang, Xue-xiu Zhong
{"title":"Uniqueness and Nondegeneracy of Positive Solutions of General Kirchhoff Type Equations","authors":"Yu-ting Kang,&nbsp;Peng Luo,&nbsp;Chang-lin Xiang,&nbsp;Xue-xiu Zhong","doi":"10.1007/s10255-023-1062-7","DOIUrl":"10.1007/s10255-023-1062-7","url":null,"abstract":"<div><p>In the present paper, we study uniqueness and nondegeneracy of positive solutions to the general Kirchhoff type equations </p><div><div><span>$$-Mleft(int_{mathbb{R}^{N}}{vertnabla vvert}^{2}dxright)Delta v=g(v) quad {rm in};{mathbb{R}^{N}},$$</span></div></div><p> where <i>M</i>: [0, +∞) ↦ ℝ is a continuous function satisfying some suitable conditions and <i>v</i> ∈ <i>H</i><sup>1</sup>(ℝ<sup><i>N</i></sup>). Applying our results to the case <i>M</i>(<i>t</i>) = <i>at</i> + <i>b, a, b</i> &gt; 0, we make it clear all the positive solutions for all dimensions <i>N</i> ≥ 1. Our results can be viewed as a generalization of the corresponding results of Li et al. [JDE, 2020, 268, Section 1.2].</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"414 - 424"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Regularization Smoothing Newton Method for the Symmetric Cone Complementarity Problem with the Cartesian P0-property
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0007-8
Xiang-jing Liu, San-yang Liu
{"title":"A Regularization Smoothing Newton Method for the Symmetric Cone Complementarity Problem with the Cartesian P0-property","authors":"Xiang-jing Liu,&nbsp;San-yang Liu","doi":"10.1007/s10255-025-0007-8","DOIUrl":"10.1007/s10255-025-0007-8","url":null,"abstract":"<div><p>In this paper, we consider the symmetric cone linear complementarity problem with the Cartesian <i>P</i><sub>0</sub>-property and present a regularization smoothing method with a nonmonotone line search to solve this problem. It has been demonstrated that the proposed method exhibits global convergence under the condition that the solution set of the complementarity problem is nonempty. This condition is less stringent than those that have appeared in some existing literature. We also show that the method has locally quadratic convergence under appropriate conditions. Some experimental results are reported to illustrate the efficiency of the proposed method.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"556 - 572"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global Existence and Boundedness for the Attraction-repulsion Keller-Segel Model with Volume Filling Effect
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0020-y
Jian Deng
{"title":"Global Existence and Boundedness for the Attraction-repulsion Keller-Segel Model with Volume Filling Effect","authors":"Jian Deng","doi":"10.1007/s10255-025-0020-y","DOIUrl":"10.1007/s10255-025-0020-y","url":null,"abstract":"<div><p>This paper is concerned with the attraction-repulsion Keller-Segel model with volume filling effect. We consider this problem in a bounded domain Ω ⊂ ℝ<sup>3</sup> under zero-flux boundary condition, and it is shown that the volume filling effect will prevent overcrowding behavior, and no blow up phenomenon happen. In fact, we show that for any initial datum, the problem admits a unique global-in-time classical solution, which is bounded uniformly. Previous findings for the chemotaxis model with volume filling effect were derived under the assumption 0 ≤ <i>u</i><sub>0</sub>(<i>x</i>) ≤ 1 with <i>ρ</i>(<i>x,t</i>) ≡ 1. However, when the maximum size of the aggregate is not a constant but rather a function <i>ρ</i>(<i>x,t</i>), ensuring the boundedness of the solutions becomes significantly challenging. This introduces a fundamental difficulty into the analysis.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"513 - 524"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Lindley-Weibull Distribution
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-04-02 DOI: 10.1007/s10255-025-0003-z
Jun-mei Jia, Zai-zai Yan, Xiu-yun Peng
{"title":"The Lindley-Weibull Distribution","authors":"Jun-mei Jia,&nbsp;Zai-zai Yan,&nbsp;Xiu-yun Peng","doi":"10.1007/s10255-025-0003-z","DOIUrl":"10.1007/s10255-025-0003-z","url":null,"abstract":"<div><p>In this paper, a new distribution named the Lindley-Weibull distribution which combines Lindley and Weibull distributions by using the method of T-X family is introduced. This distribution offers a more flexible model for lifetime data. We study its statistical properties include the shapes of density and hazard rate, residual and reversed residual lifetime, moment, moment generating functions, conditional moment, conditional moment generating, quantiles functions, mean deviations, Rényi entropy, Bonferroni and Loren curves. The distribution is capable of modeling increasing, decreasing, upside-down bathtub and decreasing-increasing-decreasing hazard rate functions. The method of maximum likelihood is adopted for estimating the model parameters. The potentiality of the new model is illustrated by means of one real data set.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 2","pages":"588 - 600"},"PeriodicalIF":0.9,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143749197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multiply robust estimation of causal effects using linked data
IF 1.5 3区 数学
Computational Statistics & Data Analysis Pub Date : 2025-04-02 DOI: 10.1016/j.csda.2025.108175
Shanshan Luo , Yechi Zhang , Wei Li , Zhi Geng
{"title":"Multiply robust estimation of causal effects using linked data","authors":"Shanshan Luo ,&nbsp;Yechi Zhang ,&nbsp;Wei Li ,&nbsp;Zhi Geng","doi":"10.1016/j.csda.2025.108175","DOIUrl":"10.1016/j.csda.2025.108175","url":null,"abstract":"<div><div>Unmeasured confounding presents a common challenge in observational studies, potentially making standard causal parameters unidentifiable without additional assumptions. Given the increasing availability of diverse data sources, exploiting data linkage offers a potential solution to mitigate unmeasured confounding within a primary study of interest. However, this approach often introduces selection bias, as data linkage is feasible only for a subset of the study population. To address such a concern, this paper explores three nonparametric identification strategies assuming that a unit's inclusion in the linked cohort is determined solely by the observed confounders, while acknowledging that the ignorability assumption may depend on some partially unobserved covariates. The existence of multiple identification strategies motivates the development of estimators that effectively capture distinct components of the observed data distribution. Appropriately combining these estimators yields triply robust estimators for the average treatment effect. These estimators remain consistent if at least one of the three distinct parts of the observed data law is correct. Moreover, they are locally efficient if all the models are correctly specified. The proposed estimators are evaluated using simulation studies and real data analysis.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"209 ","pages":"Article 108175"},"PeriodicalIF":1.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143769157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modularized data-driven approximation of the Koopman operator and generator
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2025-04-02 DOI: 10.1016/j.physd.2025.134651
Yang Guo , Manuel Schaller , Karl Worthmann , Stefan Streif
{"title":"Modularized data-driven approximation of the Koopman operator and generator","authors":"Yang Guo ,&nbsp;Manuel Schaller ,&nbsp;Karl Worthmann ,&nbsp;Stefan Streif","doi":"10.1016/j.physd.2025.134651","DOIUrl":"10.1016/j.physd.2025.134651","url":null,"abstract":"<div><div>Extended Dynamic Mode Decomposition (EDMD) is a widely-used data-driven approach to learn an approximation of the Koopman operator. Consequently, it provides a powerful tool for data-driven analysis, prediction, and control of nonlinear dynamical (control) systems. In this work, we propose a novel modularized EDMD scheme tailored to interconnected systems. To this end, we utilize the structure of the Koopman generator that allows to learn the dynamics of subsystems individually and thus alleviates the curse of dimensionality by considering observable functions on smaller state spaces. Moreover, our approach canonically enables transfer learning if a system encompasses multiple copies of a model as well as efficient adaption to topology changes without retraining. We provide probabilistic finite-data bounds on the estimation error using tools from graph theory. The efficacy of the method is illustrated by means of various numerical examples.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134651"},"PeriodicalIF":2.7,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Power-enhanced two-sample mean tests for high-dimensional microbiome compositional data.
IF 1.4 4区 数学
Biometrics Pub Date : 2025-04-02 DOI: 10.1093/biomtc/ujaf034
Danning Li, Lingzhou Xue, Haoyi Yang, Xiufan Yu
{"title":"Power-enhanced two-sample mean tests for high-dimensional microbiome compositional data.","authors":"Danning Li, Lingzhou Xue, Haoyi Yang, Xiufan Yu","doi":"10.1093/biomtc/ujaf034","DOIUrl":"10.1093/biomtc/ujaf034","url":null,"abstract":"<p><p>Testing differences in mean vectors is a fundamental task in the analysis of high-dimensional microbiome compositional data. Existing methods may suffer from low power if the underlying signal pattern is in a situation that does not favor the deployed test. In this work, we develop 2-sample power-enhanced mean tests for high-dimensional compositional data based on the combination of $P$-values, which integrates strengths from 2 popular types of tests: the maximum-type test and the quadratic-type test. We provide rigorous theoretical guarantees on the proposed tests, showing accurate Type-I error rate control and enhanced testing power. Our method boosts the testing power toward a broader alternative space, which yields robust performance across a wide range of signal pattern settings. Our methodology and theory also contribute to the literature on power enhancement and Gaussian approximation for high-dimensional hypothesis testing. We demonstrate the performance of our method on both simulated data and real-world microbiome data, showing that our proposed approach improves the testing power substantially compared to existing methods.</p>","PeriodicalId":8930,"journal":{"name":"Biometrics","volume":"81 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143762714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Equivariant birational geometry of cubic fourfolds and derived categories
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2025-04-02 DOI: 10.1016/j.aim.2025.110249
Christian Böhning , Hans-Christian Graf von Bothmer , Yuri Tschinkel
{"title":"Equivariant birational geometry of cubic fourfolds and derived categories","authors":"Christian Böhning ,&nbsp;Hans-Christian Graf von Bothmer ,&nbsp;Yuri Tschinkel","doi":"10.1016/j.aim.2025.110249","DOIUrl":"10.1016/j.aim.2025.110249","url":null,"abstract":"<div><div>We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"469 ","pages":"Article 110249"},"PeriodicalIF":1.5,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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